Proceedings of the 11th Int. Symposium Application of Laser Techniques to Fluid Mechanics. Lisbon. July 2002
by
D. Santana (1) , A. Lecuona, J. Nogueira, A. Macías-Machín (2)
Universidad Carlos III de Madrid. Area de Ingeniería Térmica
Avda. de la Universidad 30, 28911 Leganes, Madrid, Spain.
(2) Universidad de Las Palmas de Gran Canaria, Campus de Tafira Alta, s/n Las Palmas de Gran Canaria, Spain.
(1) Corresponding autor:dsantana@ing.uc3m.es
ABSTRACT
This paper presents preliminary results about Particle Image Velocimetry applications to initial particle velocity determination on bubble eruptions in a 2-D freely bubbling fluidized beds. A two-dimensional non-reacting fluidized bed was constructed with the aim to measure the origin of ejected particles and the initial particle velocity distribution in a freely fluidized bed using coarse sand particles. The bubble ejection mechanism was observed taking into account not only the origin of particles ejected but also the initial particle velocity distributions as well as the effect of other neighboring exploding bubbles. Our results, show that the assumption of initial velocity linear dependence with the angle predicts fidelity only the velocity for purely vertical ascent bubbles at low angles. Measurements of ejection velocities show that initial velocities in the combined layer are well higher than the particles in the nose of the leading bubble. Then, avoiding the coalescence of bubbles at the bed surface can lead to less particle entrainment out the bed and then lower fluidized beds.

1.INTRODUCTION
There are several techniques for gas-solid reaction available, but fluidized beds yields the greatest rate of reaction per reactor volume, mainly due to high contact area between particles and gas. Thus, it is not a surprise finding a wide range of applications of this technique such as combustion, gasification, incineration, cracking catalysis, etc…
The flow in a fluidized bed is very complex for its two-phase non-steady 3D characteristics. Hence experimental measurements and numerical models are far from complete.
One of the most important problems of fluidized beds is the entrainment and/or elutriation of particles. Entrainment and elutriation are technical terms used interchangeably to describe the loss of inert particles and/or fuel in a fluidized bed system. Normally, entrainment is the carryover of large ejected particles by the gas flow field, and eventually, the particles will fall back to the bed surface because of their high terminal velocities. Elutriation is normally used to describe the fractional carryover of finer particles when the bed particles size distribution is wide.
Particle elutriation and entrainment are extremely complex phenomena, which are not well understood from a dynamics viewpoint (Jan de Korte et al. 2001). Most of the available information consists on correlation of experimental data giving elutriation rate as a function of physical characteristics of gas and particles, besides operating conditions.
Information about particle dynamics when ejected from bubble eruption at the open surface of the bed and its path along the freeboard are needed to properly model the entrainment flux.
The entrainment flux simulations for freely gas-solid fluidized beds are based on particle trajectories in the freeboard.
Then, the initial particle velocity distributions by the bubble eruption at the bed surface must be known. An accurate prediction of initial particle velocities and gas velocity field can lead to a more precise determination of particle concentrations along the freeboard and as consequence, reliable design of filter equipments such as cyclones, scrubbers, bag filters, etc…
Initial particle velocity distribution at the bed open surface are crucial to the accurate prediction of the particle trajectory in the freeboard and for the determination of the maximum height attained by the ejected particles. It is believed that the initial particle velocity has a distribution in the vertical direction. Peters and Prybylowski 1983 assumed that the initial particle angular velocity distribution was constant in the direction normal to the bubble surface right at the moment of bubble bursting. Demmich 1984 suggested that the particle velocity distribution along the circumference of the bubble nose should be a an exponential function instead of a constant distribution. However, no concrete velocity distribution was given. On the other hand, Fung and Hamdullahpur 1993 assumed that angular particle ejection velocity decreases linearity with the bubble angle. Neither of these authors present experimental results about initial particle velocity even though a clear definition of initial particle velocity.
Most of the available results about the initial particle velocity distribution are related to the origin of ejected particles and the bubble eruption mechanism (Levy et al. 1983). These results are obtained from measurements in eruptions of bubbles injected in narrow fluidized beds with coarse particles. But the size of bubbles produced by a given gas injection is very sensitive to both overall flow rate and degree of packing or disturbance in the dense phase, at least with some materials. Therefore it is difficult to translate data of initial particle velocities obtained from carefully injected bubbles to initial particle velocities and origin of ejected particles in freely bubbling fluidized beds. These results about origin of ejected particles and bubbles dynamics in fluidized beds have been carried successfully in 2D fluidized beds instead of 3D fluidized beds due to in 3D fluidized beds visual observations of bubble dynamics are impossible today.
Early measurements in fluidized beds were restricted to the freeboard region using point measurements techniques, such as Laser Doppler Anemometry (LDA) and Hot Wire Anemometry (Pemberton and Davidson, 1984) These yield a time history at a point in the bed, normally far of the bed surface, from which mean and RMS-fluctuation velocities can be calculated. However, a disadvantage is that readings at different points in the flow are not simultaneous. If the flow being measured is reproducible, then this is not a problem, but if the velocity fluctuation are as large and as chaotic as appear to be above fluidized bed, the measurements of gas and/or particles velocities at different positions in the freeboard and/or the bed surface, taken at different times, may not be fully comparable because the flow fields might not be identical.
Therefore, PIV techniques are progressively used to explain the fluidization phenomenon. The fist application of PIV to fluidization was made by Rix et al. (1996), this experiments were restricted to determination of gas field in the freeboard above a erupting bubble far from the bed surface. Posteriorly, Yórquez-Ramírez and Duursma (2000-2001)

and Duursma et al. (2001) studied the air flow pattern above and erupting bubble in a incipiently fluidized bed, showing the applicability of PIV techniques to obtain air flow fields in fluidized beds.
A two-dimensional non-reacting fluidized bed 1m wide was constructed with the aim to measure the origin of ejected particles and the initial particle velocity distribution in a freely fluidized bed using coarse sand particles. The bubble ejection mechanism was observed taking into account not only the origin of ejected particles but also the initial particle velocity distributions as well as the effect of other neighboring exploding bubbles. Images for different bubble eruption mechanism were selected, both isolated and affected by other neighbor exploding bubbles.
The PIV measurements here reported are of the particles sliding on the surface of the glass sheet end walls. Questions arise on the validity of the velocity obtained, as representative of the velocity of the particles inside the bed. Solid friction could drag these particles behind. This does not seen the case, as the interface of the bubbles seems neatly perpendicular to the end walls. Besides that, end wall friction could be not enough to separate contacting particles, as a consequence of a higher entrainment by the free neighbor particles, but the whole aggregate could be changed. This point is still unclear and under investigation.
This paper presents preliminary results about Particle Image Velocimetry applications to initial particle velocity determination on bubble eruptions in a 2-D freely bubbling fluidized beds.
2.EXPERIMENTAL
A two-dimensional fluidized bed of dimensions 100x100x0.5 cm was constructed from glass. The solids in the bed was fluidized by compressed air supplied from the mains. A plate with 100 orifices 1mm diameter served as a distributor. A plenum 30 cm height with a predistributor was mounted to ensure a uniform air velocity distribution at entrance to the plate distributor.
Quartz sand particles with mean diameter 300 µ m was used as fluidizing medium. The settled bed depth was fixed 14 cm with a minimum fluidizing velocity of 57.3 cm/s. All the experiments presented here were carried out at 160 cm/s in bubbling free regime, avoiding the particles entrainment out of the fluidized bed since particles terminal velocities were higher than the superficial gas velocity.
The bed was uniformly illuminated by a continuous light source and the bubble approach to surface and bubble eruptions images were captured using a Kodak Motion Corder Analyzed SR series CCD video camera at a rate of 250
Hz. The imaged area was 15x16 cm (480x512 pixels).
Series of recorded bubble eruptions were analyzed via correlations based LFC-PIV technique (Nogueira et al. 2001). A
4 pixels grid distance was selected for the vectors measurement. This makes the effective window side size around 8 pixels. The number of iterations of the LFC-PIV system varied from 3 to 5 depending on the case. This allows for the description of 3 wavelength features (Lecuona et al 2002).
We are only interest in the evolution of the bulge layers then, a global threshold to the images were applied and only vectors in the bulge layer and in the combined layer are presented. This can be accomplished readily due to the emulsion phase possesses higher intensity values in comparisons to the bubble phase.
3.RESULTS AND DISCUSSION
3.1 Mechanism of solid ejection
For the operating conditions used in the experiments, the most important solid ejection mechanisms the bubble coalescence at the bed surface was shown. When bubbles coalesce at the bed surface a series of events occurs. The bulge layer of the leading bubble stretches and moves upward as the bubble approaches the bed surface becoming leaner. After rising to a maximum height somewhat less than the bubble diameter, the bubble particles fall back to the bed surface, actually toward the bubble inside. The bulge material of the leading bubble is thrown above the bed as a result of the nose layer breakup. The layer of solids between the bubbles combines with the leading bubble bulge layer; the resulting particle could expands upward and outward through the channel open by the leading bubble and falls back to the bed surface. Figure 1 depicts this phenomenon.

(a) (b)
(c)
Figure1: Mechanism of solids ejection (particles in white)
(a) leading bubble approaching the bed surface
(d)
(b) bubble erupting at bed surface
(c) Combined layer of solids growing in size
(d) Combined layer of solids ejection
3.2 Initial particle velocity for the leading bubble
Figure 2 shows the evolution of the bubble nose velocity while the particle layer of the bubble stretches and expands at the bed surface, for clearness are represented only vector evolution at the bubble nose.
As the bubble approaches the bed surface the particles at the top bubble nose are accelerating upward whilst particles at the bottom are decelerating and falling off inside the bubble. Through this mechanism the bubble nose layer becomes thinner and thus lighter and we can define the initial particles velocity as the velocity at which particles begin to behave individuality rather than particle aggregates.

Figure 2. Velocity evolution of leading bubble layer
Also, in figure 2 shows how bubble nose area increases above the bed surface, the top bubble nose accelerates in all directions except in the region of nose near the bed surface,. when the bubble nose is near the bed surface level. The acceleration is small as far as the bubble mass center is at the bed surface level, the bubble nose accelerate until bubble nose layer become more porous and particles are ejected to the bed freeboard. At this instant is where we define the initial particle ejection velocity (slices in blue in figure 2).
Measurements of initial particle ejection velocity distributions do not exits in the literature but various authors have proposed distributions from a theoretical point of view. Peters and Prybylowski 1983 proposed a uniform initial ejection velocity distribution along the bubble nose surface (high angle), taking into account the porosity variation from bubble nose center (null angle) to bubble nose near the bed surface, Demmich 1984 supposed an exponential distribution based on force balance at the bubble nose layer while Fung and Hamdullahpur 1993 proposed that the radial particle ejection velocity on the bubble circumference is such that ejection velocity decrease linearity with the angle. Therefore, the initial particle distribution can be estimate as a sine-cosine function:
U
U max
=

 1 −
θ
θ max

 cos
( )
(1)
V
=

 1 −
θ
θ max

 sin
( )
(2)
U max where θ max
is the maximum particle ejection angle, U and V are the vertical and horizontal velocity vector components respectively and U max
is the maximum vertical velocity along the bubble nose.
Among these initial particle ejection velocity distributions, the linear assumption seems more appropriate than the others for our ejection velocities, results of the PIV measurements performed. As one can see in figure 3, Fung and
Hamdullahpur 1993 assumed distribution in much the same way the experimental ejection velocities for a bubble erupting vertically.

Figure 3. Vertical ejection particle velocity
As regards to the horizontal ejection velocity distribution, linear assumption is not as appropriate as for vertical ejection velocity, predicts poorly the velocity at bubble nose top. As can be show in figure 4, experimental velocities evidence that only particles up in the supporting layer of the bubble nose have horizontal velocities comparable to vertical velocities whilst particles on bubble nose top have negligible horizontal velocity component, thus giving a purely vertical motion.
The experimental results show that this is only valid for bubbles approaching vertically to the bed surface For bubbles approaching in a different direction we have not found particle ejection velocity distributions witch predicts our velocities measurements yet (measurements not represent here).
Figure 4. Horizontal ejection particle velocity

3.3 Particle velocities for the trailing bubble
The velocity evolution of the combined layer between the leading and trailing bubble in shown in figure 5. The wake of the leading bubble acts as a bed surface for the trailing bubble nose (a). In proportion as the trailing bubble approach to the leading bubble combined layer accelerate through the channel open by the leading bubble (b), reaching a maximum velocity when the combined layer reach the divergent channel open by the leading bubble (c), progressively the combined layer decelerate catching particles ejected by the leading bubble (d).
(a) (b)
(c) (d)
Figure 5. Velocity of the combined layer
CONCLUSIONS
It has been possible to measure individual al assembled particles velocities using standard correlation PIV in an opaque two-phase flow of a bubbling fluidized bed. The linear dependence with the angle of the velocity predicts well the initial ejection velocities for a bubble erupting vertically and for low angles. For higher angles the particles move parallels to the bed surface with a negligible vertical velocity vector. Particles in the combined layer possess ejection velocities in great extent of particles ejected from leading bubble nose.

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